A NOTE ON FRACTIONAL KDV HIERARCHIES

One of the cornerstones of the theory of integrable systems of KdV typ e has been the remark that the n-GD (Gel'fand-Dickey) equations are re ductions of the full Kadomtsev-Petviashvilij (ICP) theory, In this pap er we address the analogous problem for the fractional KdV theories, b y suggesting candidates of the ''KP theories'' lying behind them, Thes e equations are called ''KP(m) hierarchies,'' and are obtained as redu ctions of a bigger dynamical system, which we call the ''central syste m.'' The procedure allowing passage from the central system to the KP( m) equations, and then to the fractional KdV(n)(m) equations, is discu ssed in detail in the paper. The case of KdV(3)(2) is given as a parad igmatic example. (C) 1997 American Institute of Physics.